Related papers: Convergence Analysis of Data Augmentation Algorith…
Multiple imputation has become one of the standard methods in drawing inferences in many incomplete data applications. Applications of multiple imputation in relatively more complex settings, such as high-dimensional clustered data, require…
This paper tackles the problem of robust covariance matrix estimation when the data is incomplete. Classical statistical estimation methodologies are usually built upon the Gaussian assumption, whereas existing robust estimation ones assume…
The logistic regression model is the most popular model for analyzing binary data. In the absence of any prior information, an improper flat prior is often used for the regression coefficients in Bayesian logistic regression models. The…
Gaussian Mixture models (GMMs) are a powerful tool for clustering, classification and density estimation when clustering structures are embedded in the data. The presence of missing values can largely impact the GMMs estimation process,…
Data augmentation improves the convergence of iterative algorithms, such as the EM algorithm and Gibbs sampler by introducing carefully designed latent variables. In this article, we first propose a data augmentation scheme for the…
Data augmentation is an essential part of the training process applied to deep learning models. The motivation is that a robust training process for deep learning models depends on large annotated datasets, which are expensive to be…
The data augmentation (DA) algorithms are popular Markov chain Monte Carlo (MCMC) algorithms often used for sampling from intractable probability distributions. This review article comprehensively surveys DA MCMC algorithms, highlighting…
Deep Learning (DL) methods have emerged as one of the most powerful tools for functional approximation and prediction. While the representation properties of DL have been well studied, uncertainty quantification remains challenging and…
In this short note, we consider posterior simulation for a linear regression model when the error distribution is given by a scale mixture of multivariate normals. We first show that the sampler of Backlund and Hobert (2020) for the case of…
We use the theory of normal variance-mean mixtures to derive a data-augmentation scheme for a class of common regularization problems. This generalizes existing theory on normal variance mixtures for priors in regression and classification.…
Recently, high-dimensional heterogeneous data have attracted a lot of attention and discussion. Under heterogeneity, semiparametric regression is a popular choice to model data in statistics. In this paper, we take advantages of expectile…
The use of MCMC algorithms in high dimensional Bayesian problems has become routine. This has spurred so-called convergence complexity analysis, the goal of which is to ascertain how the convergence rate of a Monte Carlo Markov chain scales…
We provide universality results that quantify how data augmentation affects the variance and limiting distribution of estimates through simple surrogates, and analyze several specific models in detail. The results confirm some observations…
Generalized linear mixed models (GLMMs) are often used for analyzing correlated non-Gaussian data. The likelihood function in a GLMM is available only as a high dimensional integral, and thus closed-form inference and prediction are not…
Data augmentation (DA) algorithms are widely used for Bayesian inference due to their simplicity. In massive data settings, however, DA algorithms are prohibitively slow because they pass through the full data in any iteration, imposing…
Seemingly unrelated linear regression models are introduced in which the distribution of the errors is a finite mixture of Gaussian components. Identifiability conditions are provided. The score vector and the Hessian matrix are derived.…
In this work, we consider the problem of imbalanced data in a regression framework when the imbalanced phenomenon concerns continuous or discrete covariates. Such a situation can lead to biases in the estimates. In this case, we propose a…
Missing data arises when certain values are not recorded or observed for variables of interest. However, most of the statistical theory assume complete data availability. To address incomplete databases, one approach is to fill the gaps…
Data augmentation plays a pivotal role in enhancing and diversifying training data. Nonetheless, consistently improving model performance in varied learning scenarios, especially those with inherent data biases, remains challenging. To…
Non-Gaussian and multimodal distributions are an important part of many recent robust sensor fusion algorithms. In difference to robust cost functions, they are probabilistically founded and have good convergence properties. Since their…